Verification of polyhedral optimizations with constant loop bounds in finite state space computations

Abstract

As processors gain in complexity and heterogeneity, compilers are asked to perform program transformations of ever-increasing complexity to effectively map an input program to the target hardware. It is critical to develop methods and tools to automatically assert the correctness of programs generated by such modern optimizing compilers. We present a framework to verify if two programs (one possibly being a transformed variant of the other) are semantically equivalent. We focus on scientific kernels and a state-of-the-art polyhedral compiler implemented in ROSE. We check the correctness of a set of polyhedral transformations by combining the computation of a state transition graph with a rewrite system to transform floating point computations and array update operations of one program such that we can match them as terms with those of the other program. We demonstrate our approach on a collection of benchmarks from the PolyBench/C suite.